Silicon (monocrystalline, polycrystalline, amorphous silicon) can be named as material mainly used in the MEMS filter. The silicon is widely used not only for its compatibility to the IC process, but also for its superior mechanical and electrical characteristics, and various methods are proposed for filter excitation and detection methods. Among a large number of methods, a filter using capacitance type resonators can be manufactured comparatively easily using silicon micromachining process, and therefore well suited for realization of the GHz-band MEMS filter.
Mainly, the current capacitance type MEMS filter has a structure wherein a large number of MEMS resonators are joined mechanically by a microsize beam, etc., and the center frequency of the filter is determined by the resonating frequency of the constituent MEMS resonators. When a certain number of MEMS resonators are connected, the number of frequency mode peaks that appears are equivalent to the number of the MEMS resonators connected, each with distinct mode shape that are different in phase. The frequency bandwidth of the MEMS filter is determined by a spring constant kcij of a coupling element for joining the resonators and a spring constant krc, which is the connecting part of the MEMS resonator and the coupling element.
Non-patent document 1 shows an example of a capacitance type MEMS filter, wherein a structure of joining two polycrystalline silicon doubly-clamped beam MEMS resonators is used. The results of Q value 40 to 450, frequency bandwidth 0.2% to 2.5%, insertion loss 2 dB or less with the center frequency of the filter as 8 MHz are achieved. The design specifications of the MEMS resonator are 40.8 μm in length, 8 μm in width, and 1.2 μm in thickness and the coupling beam is formed with the dimensions of 20.35 μm in length, 0.75 μm in width, and 1.2 μm in thickness comparatively close to those of the resonator. If the MEMS resonator and the beam as the coupling element for joining the MEMS resonators are formed with equivalent microsize dimensions and a length coupling element as less than one-eighth wavelength λ as in non-patent document 1, the mass of the coupling element is added to the mass of the MEMS resonator and the shifting of center frequency of the filter may result. Such mass loading effects are reflected on the filter characteristic, so that any desired passband waveform may not be obtained.
Non-patent document 2 illustrates an example of joining three MEMS resonators mechanically, and this case is shown as a block diagram of FIG. 28. A first MEMS resonator 10, a second MEMS resonator 12, and a third MEMS resonator 14 are contained and a first coupling beam 16 and a second coupling beam 18 for connecting them are further contained. FIG. 29 shows an electric equivalent circuit to FIG. 28 and corresponds to the case where the first and second coupling beams 16 and 18 are formed as a length of λ/8 or less. Numerals 20, 22, and 24 denote the first to third MEMS resonators 10, 12, and 14, and numerals 26 and 28 denote the first and second coupling beams 16 and 18. In FIG. 29, the mass of the first coupling beam 16 is indicated by inductor L26a, 26b, the mass of the second coupling beam 18 is indicated by inductor L28a, 28b, and the value of each L becomes equal to a half of the static mass of the coupling beam.
As shown in expression 3, ZL represents the impedance of the inductor L, w represents the resonating frequency, and M1 represents the static mass of the coupling beam. Spring constants 26c and 28c of the coupling beams are represented each by the reciprocal of a capacitor C. When this is shown in expression 4, ZC represents the impedance of the capacitor C and k1 represents a static spring constant of the coupling beam.ZL=jwL=jw(M1/2); w=2πf  [Expression 3]ZC=1/jwC=k1/jw; w=2πf  [Expression 4]
FIG. 30 shows an example of the passband waveform of the three-stage MEMS filter. If the mass of the coupling beams can be ignored, the passband waveform should represent a waveform close to an ideal waveform 30; however, the mass of second MEMS resonator 12 is increased due to the mass effect of the first and second coupling element beams 16 and 18 joining to the left and the right of the resonator 12 as compared with the first MEMS resonator and the third MEMS resonator, leading to the result having a distorted waveform 32, etc. From such a problem, the author of non-patent document 2 proposes the following two methods:
In one of the methods, the coupling element is designed as a length of λ/4, whereby 26a, 26b of the coupling element 26 shown in the equivalent circuit in FIG. 29 is replaced with a minus value of the capacitor C of 26c. Accordingly, the mass of the coupling beam does not appear in the characteristic of the MEMS filter. In another method, the design of connecting the coupling element and the MEMS resonator is proposed. The coupling beam is joined at the coupling node of the MEMS resonator where the vibration amplitude at the resonance is small, whereby large values of MEMS resonator mass mrc and spring constant krc are obtained at the connection part of the MEMS resonator capered to the mass mcij and the spring constant kcij of the coupling beam, and as a result the mass loading effects can be minimized in this method.
Patent document 1 has a structure containing a radial contour mode disk type MEMS resonator with a resonating frequency of to 1 GHz. In the radial contour mode, the disk vibrate symmetrically and radial along the perimeter with the center of the disk as a node, and electrode is provided in the surrounding of the disk. Vibration is produced by an electrostatic force, and the vibration capacitor change ratio is detected. The disk type resonator can also be applied to the MEMS filter and coupling element having a beam or a U shape are provided.    Non-patent document 1: Frank Bannon III, John R. Clark, C. T.-C. Nguyen, “High-Q HF Micromechanical Filters,” IEEE Journal of Solid-State Circuits, vol. 35, no. 4, 2000    Non-patent document 2: Ku Wang, C. T.-C. Nguyen, “Higher Order Medium Frequency Micromechanical Electronic Filters,” Journal of Microelectromechanical Systems, vol. 8, no. 4, 1999    Patent document 1: U.S. Pat. No. 6,628,177